I want to like these resources, but they seem to suffer from the common approach to teaching mathematics.
Namely, a complete disregard for a numerical approach, and sprinkling latex symbols throughout large blocks of text without a clear through line.
Reading education material like this feels like reading code from an llm. I am spending more time cross referencing and checking the statements than doing the thing I came to the material to work on.
> If we interpret the path integral in terms of the Wiener measure, then it does in fact solve our Wick-rotated Schrödinger equation.
I guess I’ll takes your word for it.
If you understand the material as well as your word count suggests than why omit numerical elucidation?
If you are unable to perform numerical analysis of these formulae than why should I trust your symbol mangling of them?
I do appreciate the feedback. (And I should mention that there is a supplement to the thermodynamics article that this post is about which goes through some numerical experiments; you can see it here: https://nicf.net/articles/toy-thermodynamic/.) I do think that this may just be a situation where the thing I made isn't the thing you wanted, which is fine, but I can say a little bit about why I made the decisions I made.
The audience that I had in mind for these pieces is mostly people who've had some amount of training in pure math; it came about because I felt (and still feel) like a lot of the existing resources for this stuff aren't presented in a way that lines up well with the way that people with that training often like to absorb information.
Speaking for myself, I don't think I would enjoy reading an article about the Feynman path integral that's full of tables and graphs with results of numerical experiments. My reaction to a piece like that would be "Okay, that's nice, but can you please just say what mathematical objects we're even talking about here first?" It sounds like you have the opposite set of expectations, which is totally fine, and that probably just means these aren't the articles for you, but there (I hope!) are also other people whose expectations are more in alignment with the presentation I went for. I don't think either of us is "wrong"; our preferences are just different.
This is such a beautiful reply. I am bookmarking it. There is value in distilling out the key abstractions that wants to be heard from the sea of data.
Standard results omitting tedious derivations is a standard practice in all educational material of upper level physics. "Derivation left to reader", etc. I personally greatly enjoy the fact that i get to decide how much detail i want. I can get the gist, a moderate exploration, or a deep dive if i have the time. Keep in mind, this person did not have to make this resource, and if you don't like it you don't have to read it. I greatly appreciate a breadth of resources when learning a topic and this is an amazing addition to my learning resources. If you absolutelyneed every single detail of every single assertion then look it up, but i can never expect a human doing this in their free time as a free gift to write dozens of textbooks about every facet of physics. Keeping every single detail in would make these prohibitively time consuming to create in a way that i don't think a free resource could support
I want to like these resources, but they seem to suffer from the common approach to teaching mathematics.
Namely, a complete disregard for a numerical approach, and sprinkling latex symbols throughout large blocks of text without a clear through line.
Reading education material like this feels like reading code from an llm. I am spending more time cross referencing and checking the statements than doing the thing I came to the material to work on.
> If we interpret the path integral in terms of the Wiener measure, then it does in fact solve our Wick-rotated Schrödinger equation.
I guess I’ll takes your word for it.
If you understand the material as well as your word count suggests than why omit numerical elucidation?
If you are unable to perform numerical analysis of these formulae than why should I trust your symbol mangling of them?